Ratio and Unitary Method Worksheet for Olympiad

Maths Olympiad topic 13: Ratio and the unitary method · Set 531 · 40 questions

How to solve it (Go through one): Unitary: cost of one = total ÷ number; then multiply by how many you need. Ratio p : q of a total: one part = total ÷ (p + q); a share = its parts × one part. Workers and days go the opposite way: total work = workers × days; days = total work ÷ new number of workers.

1. 1.₹299 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹115 (b) ₹207 (c) ₹184 (d) ₹23
2. 2.₹99 is shared between two friends in the ratio 1 : 8. How much is the bigger share? (a) ₹88 (b) ₹89 (c) ₹11 (d) ₹99
3. 3.₹187 is shared between two friends in the ratio 2 : 9. How much is the bigger share? (a) ₹34 (b) ₹153 (c) ₹170 (d) ₹17
4. 4.7 workers can build a wall in 12 days. How many days will 4 workers take, working at the same speed? (a) 9 days (b) 21 days (c) 15 days (d) 22 days
5. 5.If 2 pens cost ₹6, how much do 4 pens cost? (a) ₹15 (b) ₹8 (c) ₹12 (d) ₹24
6. 6.6 workers can build a wall in 9 days. How many days will 3 workers take, working at the same speed? (a) 18 days (b) 12 days (c) 19 days (d) 6 days
7. 7.₹195 is shared between two friends in the ratio 4 : 9. How much is the bigger share? (a) ₹135 (b) ₹150 (c) ₹15 (d) ₹60
8. 8.8 workers can build a wall in 5 days. How many days will 5 workers take, working at the same speed? (a) 7 days (b) 2 days (c) 9 days (d) 8 days
9. 9.If 4 pens cost ₹92, how much do 10 pens cost? (a) ₹920 (b) ₹230 (c) ₹253 (d) ₹98
10. 10.₹504 is shared between two friends in the ratio 5 : 9. How much is the bigger share? (a) ₹180 (b) ₹36 (c) ₹252 (d) ₹324
11. 11.₹33 is shared between two friends in the ratio 1 : 2. How much is the bigger share? (a) ₹23 (b) ₹22 (c) ₹11 (d) ₹33
12. 12.If 7 pens cost ₹63, how much do 10 pens cost? (a) ₹630 (b) ₹90 (c) ₹66 (d) ₹99
13. 13.3 workers can build a wall in 11 days. How many days will 11 workers take, working at the same speed? (a) 3 days (b) 2 days (c) 4 days (d) 19 days
14. 14.5 workers can build a wall in 15 days. How many days will 3 workers take, working at the same speed? (a) 13 days (b) 9 days (c) 17 days (d) 25 days
15. 15.₹198 is shared between two friends in the ratio 4 : 5. How much is the bigger share? (a) ₹22 (b) ₹99 (c) ₹110 (d) ₹88
16. 16.₹320 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹160 (b) ₹280 (c) ₹40 (d) ₹320
17. 17.6 workers can build a wall in 9 days. How many days will 9 workers take, working at the same speed? (a) 12 days (b) 5 days (c) 7 days (d) 6 days
18. 18.4 workers can build a wall in 14 days. How many days will 8 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 18 days (d) 10 days
19. 19.6 workers can build a wall in 15 days. How many days will 2 workers take, working at the same speed? (a) 19 days (b) 5 days (c) 45 days (d) 11 days
20. 20.₹296 is shared between two friends in the ratio 1 : 7. How much is the bigger share? (a) ₹296 (b) ₹37 (c) ₹148 (d) ₹259
21. 21.If 9 kites cost ₹27, how much do 6 kites cost? (a) ₹21 (b) ₹24 (c) ₹162 (d) ₹18
22. 22.6 workers can build a wall in 14 days. How many days will 12 workers take, working at the same speed? (a) 28 days (b) 7 days (c) 8 days (d) 20 days
23. 23.9 workers can build a wall in 10 days. How many days will 2 workers take, working at the same speed? (a) 46 days (b) 3 days (c) 45 days (d) 17 days
24. 24.₹611 is shared between two friends in the ratio 5 : 8. How much is the bigger share? (a) ₹423 (b) ₹376 (c) ₹235 (d) ₹47
25. 25.₹64 is shared between two friends in the ratio 3 : 5. How much is the bigger share? (a) ₹32 (b) ₹24 (c) ₹40 (d) ₹8
26. 26.If 2 kites cost ₹8, how much do 10 kites cost? (a) ₹44 (b) ₹80 (c) ₹16 (d) ₹40
27. 27.If 4 pens cost ₹40, how much do 2 pens cost? (a) ₹30 (b) ₹80 (c) ₹20 (d) ₹38
28. 28.9 workers can build a wall in 7 days. How many days will 3 workers take, working at the same speed? (a) 21 days (b) 13 days (c) 22 days (d) 1 day
29. 29.6 workers can build a wall in 8 days. How many days will 3 workers take, working at the same speed? (a) 16 days (b) 11 days (c) 4 days (d) 5 days
30. 30.If 2 pens cost ₹8, how much do 10 pens cost? (a) ₹16 (b) ₹80 (c) ₹44 (d) ₹40
31. 31.4 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 4 days (b) 10 days (c) 6 days (d) 16 days
32. 32.If 4 kites cost ₹20, how much do 8 kites cost? (a) ₹40 (b) ₹24 (c) ₹45 (d) ₹160
33. 33.₹429 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹156 (b) ₹39 (c) ₹273 (d) ₹312
34. 34.₹440 is shared between two friends in the ratio 4 : 7. How much is the bigger share? (a) ₹280 (b) ₹160 (c) ₹40 (d) ₹220
35. 35.3 workers can build a wall in 8 days. How many days will 2 workers take, working at the same speed? (a) 12 days (b) 9 days (c) 7 days (d) 13 days
36. 36.If 8 kites cost ₹72, how much do 7 kites cost? (a) ₹71 (b) ₹72 (c) ₹504 (d) ₹63
37. 37.If 7 notebooks cost ₹105, how much do 6 notebooks cost? (a) ₹630 (b) ₹105 (c) ₹104 (d) ₹90
38. 38.If 7 pens cost ₹119, how much do 8 pens cost? (a) ₹136 (b) ₹153 (c) ₹120 (d) ₹952
39. 39.6 workers can build a wall in 11 days. How many days will 2 workers take, working at the same speed? (a) 15 days (b) 34 days (c) 33 days (d) 7 days
40. 40.If 6 notebooks cost ₹72, how much do 11 notebooks cost? (a) ₹77 (b) ₹792 (c) ₹132 (d) ₹144

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